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Whether it be physical, biological or social processes, complex systemsexhibit dynamics that are exceedingly difficult to understand or predict fromunderlying principles. Here we report a striking correspondence between thecollective excitation dynamics of a laser driven ultracold gas of Rydberg atomsand the spreading of diseases, which in turn opens up a highly controllableexperimental platform for studying non-equilibrium dynamics on complexnetworks. We find that the competition between facilitated excitation andspontaneous decay results in a fast growth of the number of excitations thatfollows a characteristic sub-exponential time dependence which is empiricallyobserved as a key feature of real epidemics. Based on this we develop aquantitative microscopic susceptible-infected-susceptible (SIS) model whichlinks the growth and final excitation density to the dynamics of an emergentheterogeneous network and rare active region effects associated to an extendedGriffiths phase. This provides physical insights into the nature ofnon-equilibrium criticality in driven many-body systems and the mechanismsleading to non-universal power-laws in the dynamics of complex systems.

Epidemic growth and Griffiths effects on an emergent network of excited atoms